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Simplifying 3 = -16t2 + 50t + 2 Reorder the terms: 3 = 2 + 50t + -16t2 Solving 3 = 2 + 50t + -16t2 Solving for variable 't'. Combine like terms: 3 + -2 = 1 1 + -50t + 16t2 = 2 + 50t + -16t2 + -2 + -50t + 16t2 Reorder the terms: 1 + -50t + 16t2 = 2 + -2 + 50t + -50t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 1 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 1 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 1 + -50t + 16t2 = 0 + -16t2 + 16t2 1 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1 + -50t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -3.125t + t2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -3.125t + -0.0625 + t2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -3.125t + t2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -3.125t + t2 = 0 + -0.0625 -3.125t + t2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -3.125t + t2 = -0.0625 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = -0.0625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = -0.0625 + 2.44140625 Combine like terms: -0.0625 + 2.44140625 = 2.37890625 2.44140625 + -3.125t + t2 = 2.37890625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.37890625 Calculate the square root of the right side: 1.542370335 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.542370335 and -1.542370335.Subproblem 1
t + -1.5625 = 1.542370335 Simplifying t + -1.5625 = 1.542370335 Reorder the terms: -1.5625 + t = 1.542370335 Solving -1.5625 + t = 1.542370335 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 1.542370335 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.542370335 + 1.5625 t = 1.542370335 + 1.5625 Combine like terms: 1.542370335 + 1.5625 = 3.104870335 t = 3.104870335 Simplifying t = 3.104870335Subproblem 2
t + -1.5625 = -1.542370335 Simplifying t + -1.5625 = -1.542370335 Reorder the terms: -1.5625 + t = -1.542370335 Solving -1.5625 + t = -1.542370335 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -1.542370335 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.542370335 + 1.5625 t = -1.542370335 + 1.5625 Combine like terms: -1.542370335 + 1.5625 = 0.020129665 t = 0.020129665 Simplifying t = 0.020129665Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.104870335, 0.020129665}
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